Related papers: Automated Mutual Explicit Induction Proof in Separ…
This paper considers KLM-style preferential non-monotonic reasoning in the setting of propositional team semantics. We show that team-based propositional logics naturally give rise to cumulative non-monotonic entailment relations. Motivated…
While most approaches to automatically recognizing entailment relations have used classifiers employing hand engineered features derived from complex natural language processing pipelines, in practice their performance has been only…
We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and…
Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than…
Visual entailment is a recently proposed multimodal reasoning task where the goal is to predict the logical relationship of a piece of text to an image. In this paper, we propose an extension of this task, where the goal is to predict the…
The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded…
A growing body of work studies how to answer a question or verify a claim by generating a natural language "proof": a chain of deductive inferences yielding the answer based on a set of premises. However, these methods can only make sound…
In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof…
Detecting semantic arguments of a predicate word has been conventionally modeled as a sentence-level task. The typical reader, however, perfectly interprets predicate-argument relations in a much wider context than just the sentence where…
We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path…
Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search…
Separation logics are a family of extensions of Hoare logic for reasoning about programs that mutate memory. These logics are "abstract" because they are independent of any particular concrete memory model. Their assertion languages, called…
In theorem provers based on dependent type theory such as Coq and Lean, induction is a fundamental proof method and induction tactics are omnipresent in proof scripts. Yet the ergonomics of existing induction tactics are not ideal: they do…
In this paper we present mutual coinduction as a dual of mutual induction and also as a generalization of standard coinduction. In particular, we present a precise formal definition of mutual induction and mutual coinduction. In the process…
The main aim of this paper is to promote a certain style of doing coinductive proofs, similar to inductive proofs as commonly done by mathematicians. For this purpose, we provide a reasonably direct justification for coinductive proofs…
In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…
In the rewriting logic framework, equational-based specifications are used to define deterministic functional behavior, abstract data types, and canonical representations of data. These specifications include a (possibly order-sorted)…
Closely related languages show linguistic similarities that allow speakers of one language to understand speakers of another language without having actively learned it. Mutual intelligibility varies in degree and is typically tested in…
We prove a completeness result for Multiplicative Exponential Linear Logic (MELL): we show that the relational model is injective for MELL proof-nets, i.e. the equality between MELL proof-nets in the relational model is exactly axiomatized…
Verification problems of programs written in various paradigms (such as imperative, logic, concurrent, functional, and object-oriented ones) can be reduced to problems of solving Horn clause constraints on predicate variables that represent…